Which of the following physical quantities has the same dimensions...

Planck's constant ($h$) can be determined from the energy of a photon, $E = h\nu$.

Dimensions of energy $E = [M L^2 T^{-2}]$
Dimensions of frequency $\nu = [T^{-1}]$
Therefore, dimensions of $h = \dfrac{[M L^2 T^{-2}]}{[T^{-1}]} = [M L^2 T^{-1}]$

Now, checking the given options:
Torque = Force $\times$ perpendicular distance $\Rightarrow [M L T^{-2}] \times [L] = [M L^2 T^{-2}]$
Angular momentum = $mvr \Rightarrow [M] \times [L T^{-1}] \times [L] = [M L^2 T^{-1}]$
Linear momentum = $mv \Rightarrow [M] \times [L T^{-1}] = [M L T^{-1}]$
Power = $\dfrac{\text{Work}}{\text{Time}} \Rightarrow \dfrac{[M L^2 T^{-2}]}{[T]} = [M L^2 T^{-3}]$

Thus, angular momentum has the same dimensions as Planck's constant.

Answer: Angular momentum